A diagrammatic categorification of the q-Schur algebra
Quantum Algebra
2012-02-08 v3
Abstract
In this paper we categorify the q-Schur algebra S(n,d) as a quotient of Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our 2-category contains Soergel's monoidal category of bimodules of type A, which categorifies the Hecke algebra H(d), as a full sub-2-category if d does not exceed n. For the latter result we use Elias and Khovanov's diagrammatic presentation of Soergel's monoidal category of type A.
Keywords
Cite
@article{arxiv.1008.1348,
title = {A diagrammatic categorification of the q-Schur algebra},
author = {Marco Mackaay and Marko Stosic and Pedro Vaz},
journal= {arXiv preprint arXiv:1008.1348},
year = {2012}
}
Comments
60 pages, lots of figures. v3: Substantial changes. To appear in Quantum Topology